The completeness of Kant's Table of Judgements and its consequences for philosophy of mathematics - a podcast by MCMP Team

Michiel van Lambalgen (Amsterdam) and Dora Achourioti (Amsterdam) give a talk at the MCMP Colloquium (9 Nov, 2011) titled "The completeness of Kant's Table of Judgements and its consequences for philosophy of mathematics". Abstract: It is a common belief among logicians that Kant's discussion of logic in his Critique of Pure Reason has little to offer to modern practitioners, since it appears to consist only of syllogistics plus some propositional inferences. Kant himself considered logic to be an integral part of the architecture of the Critique of Pure Reason, and in the Transcendental Deductions he attempted to show that the possible logical forms of judgements lead to the 12 Categories (e.g. causality) and the principles governing their use. However, if Kant's logic is indeed 'mathematically trivial and terrifyingly narrow-minded', as one commentator put it, then Kant's own view of his procedure is untenable. The groundwork for a revisionist view of Kant's logic has been laid by Béatrice Longuenesse's book 'Kant and the capacity to judge' (1998), which argues that Kant had indeed solid grounds for linking the Categories and logical forms of judgements. Re-reading Kant with Longuenesse's thesis in mind, one sees that Kant's logic is mathematically far from trivial. We sketch some theorems which together show that Kant's logic is 'geometric logic' (Vickers, Coquand, ...). Geometric logic is expressive enough to formalise Euclidean geometry. It's natural logic is intuitionistic, and we'll discuss the implications of this result for Kant's philosophy of mathematics.

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